Could error surface shape be useful to detect which local minima is better for generalization?
In general I agree with @nbro answer, nevertheless sticking strictly to this specific question I'd like to share some speculations: 


what the author of the question provides us with is the Loss Function Shape so I'll try to use the full information here to compare the 2 minima 
looking at the LF steepness we observe the Left LM is in a steeper region than the Right LM: how can this be interpreted? 
I'd interpret the LF Steepness as a Measure of Parametrization Stability: in fact perturbating the Parametrization slightly has a bigger effect on Left LM observed performance rather than the Right LM one 
when the NN is running "in production" typically the parametrization is fixed (in most typical application, weights are not changed out of the training phase) so you should not be concerned about parametrization stability, 
however I'm one of those believing the Flat Minima - Schmidhuber 1997 idea that Local Minima Flatness is connected to generalization property 


However it is important to observe this is still a very open and interesting question as in Sharp Minima Can Generalize For Deep Nets Dinh 2017 et al. demonstrated 
it is not just about flatness, because reparametrization of the NN model, though preserving minima locations, change its shape so basically sharp minima might be transformed into flat ones without affecting network performance